ARTICLESPUBLISHED ONLINE: 28 NOVEMBER 2010 | DOI: 10.1038/NPHYS1823

Glass transition with decreasing correlationlength during cooling of Fe50Co50 superlattice andstrong liquidsShuai Wei1, Isabella Gallino1, Ralf Busch1 and C. Austen Angell2*The glass transition is usually understood as a structural arrest that occurs during the cooling of liquids, trapping the system

before it can crystallize. It occurs for all liquid classes, including metals. Theoretical interest has focused on the dynamical

heterogeneity encountered during supercooling of ‘fragile’ liquids. Many suggest that the slow-down is caused by increasing

dynamical correlation lengths. Here we report kinetics and thermodynamics of arrest in a system that disorders while in

its ground state, exhibits a large heat capacity change (�Cp = Cp,mobile −Cp,arrested) on arrest, yet clearly is characterized by

a static correlation length that decreases when approaching the transition temperature Tg from above. We show that our

system, the Fe50Co50 superlattice, kineticallymimics an ideal ‘strong’ liquidwith a critical point. Introducing liquid critical-point

simulations, we can then argue that strong liquids differ from fragile liquids by occupying opposite flanks of an underlying

order–disorder transition, which can be continuous, critical or weakly first order.

Part of the difficulty of understanding the nature of viscousliquids and their structural arrest stems from the widelydiffering characteristics of the glass transition1,2. Although

all glass transitions are trivially associated with the crossing ofexperimental and system internal timescales, the physical signaturesof this ‘ergodicity-breaking’ event range from marked to almostinvisible. For instance, in some cases the heat capacity drops to amere 30% of its mobile state value whereas in others the drop isalmost imperceptible. Among the latter cases are the archetypal glassformer, SiO2 (dry), and its weak-field ionic cousin, BeF2.

Silica is the extreme member of a general ‘strong/fragile’ patternof viscous slow-down in glass formers, a pattern that is also foundfor the key thermodynamic property, excess entropy, when properlyscaled3. For the fragile liquids, the rate at which the structuralrelaxation time increases on cooling is much greater than expectedfrom the Arrhenius law, and the heat capacity jump at Tg is largeevenwhen scaled by the excess entropy atTg

3 (or by themore readilyavailable entropy of fusion4).

As a result of the unusual and extreme features of fragile liquids,these have received much more attention, from theoreticiansand experimentalists alike, than have strong liquids, and muchis known about their behaviour. A clear pattern of increasingheterogeneity with decreasing temperature has been observed,both in experiment5,6 (particularly near Tg) and in computersimulation7 (necessarily far above the experimental Tg for the samesort of system). As one approach to understanding the originof the slow-down, many studies have been made to detect acorrelation length that increases with decreasing temperature7–11.Both static and dynamic length scales have been under discussionand length scales have been deduced from observations of bothspontaneous fluctuations (anomalous light scattering12) and field-induced fluctuations, which are considered easier to measure11.Berthier and coauthors in particular have promoted, using aninequality (their equation (5) linking a four-point correlator to

1Materials Science and Engineering Department, Saarland University, Campus C63, 66123 Saarbrücken, Germany, 2Department of Chemistry andBiochemistry, Arizona State University, Tempe, Arizona 85287, USA. *e-mail: austenangell@gmail.com.

a measurable susceptibility11), the assumption that for molecularliquids ‘dynamic heterogeneity is strongly correlated with enthalpyfluctuations’, hence to the excess heat capacity of liquid overcrystal. On the other hand, the overarching importance of staticcorrelations has recently been stressed by Tanaka and co-workers13who demonstrate critical-like behaviour in colloids near thefragile liquid extreme14, although the correlations of importanceare not in the density.

Less attention has been given to these questions for liquids at thestrong extreme of behaviour. Somemotivation for the present workhas been provided by the realization that, for strong liquids, theexcess heat capacity varies with distance from Tg oppositely to thecase of fragile liquids15.With assistance from computer simulations,it has recently been found that both SiO2 (ref. 16) and, more clearly,BeF2 (ref. 17), have excess heat capacities that peak far above themelting point, whereas the very bad glass former, water, plays therole of Rosetta stone, being a strong liquid near its Tg but a veryfragile liquid at temperatures near and above its melting point15,18.There should, therefore, be some interest in the possibility that acorrelation length changes in the opposite direction in strong liquidcases, that is, it increases with increasing temperature above Tg andthus acts to oppose viscous slow-down.

To explore this possibility, and the much broader picture ofthe glass-former problem that it necessarily leads to, we havechosen an unusual, but we hope fruitful, approach. We study anon-liquid system,with a strong and easily studied ‘glass’ transition,in which it is known that there is a static correlation length thatchanges with temperature, and we show that this glass transitionand the associated disordering kinetics have a great deal in commonwith the behaviour of the liquids at the strong extreme of the‘strong–fragile’ liquid pattern. Thus, we have taken up the studyof an unusual binary metal superlattice system, Co50Fe50 (refs 19,20), that was first studied in the first half of the past centurywhen interest in crystalline order–disorder (λ) transitions was

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NATURE PHYSICS DOI: 10.1038/NPHYS1823 ARTICLES

Temperature (°C)

Hea

t cap

acity

(ca

l g¬1

)

Tg

T!

Endo

ther

mic

hea

t flo

w (

mW

)

Temperature (K)

910 KT (fictive)

Area = area

200 400 600 800

0.1

0.2

0.3

0.4

0

¬10

10

500 600 700 800 900 1,000

a

b

Figure 1 | The glass transition in the Fe50Co50 order–disorder transition.a, Heat capacity scan from ref. 19. Note the lambda peak (off scale) at730 ◦C and the glass transition (ergodicity-restoring) starting at about500 ◦C, when the effective heating rate is much greater than the 30K perday cooling rate. Note how the heat capacity jumps about 30% at the glasstransition (from about 10% above the classical value of 24.9 Jmol−1 K, to1.4 Cp (classical)). b, New DSC scan at 20Kmin−1 (after cooling at20Kmin−1) showing the definition of the fictive temperature fromMoynihan’s equal area construction applied to Fe50Co50, using an uppertemperature limit of 910K. The baseline is defined by the frozen sampleheat capacity, for the case, heating rate= cooling rate= 20Kmin−1.

at its height. Atypically, the ordering of Co and Fe onto theirrespective simple cubic lattices during cooling of the alloy is arrestedmidway through the transition, with a large drop, some 30%, inheat capacity (Fig. 1a).

The effect of different cooling rates (and hence ergodicity-breaking temperatures) on this glass transition was studied19 in1943, and it is qualitatively the same as observed for ionic andmolecular glass formers by Moynihan and co-workers21, andparticularly by Yue and co-workers22. In the present work we studythis phenomenology using different thermochemical protocols toextract the relaxation kinetics of the disordering process. In separateexperiments, we use an anneal-and-scan method to obtain theform of the heat capacity in the previously hidden zone below thelowest scanning Tg, and show thereby that the equilibrium heatcapacity follows the previously known ‘lambda’ form, as indeed wasto be expected. This confirms that glass transitions can occur insystems in which the heat capacity is of theoretically understoodform. More important is that we can argue that the kinetics ofordering in systems of this type are similar to the kinetics of orderingin ‘strong’ liquids so we can then argue that ordering in ‘strong’

700 750 800Temperature (K)

850 900

10

15

20

25

30

35

Endo

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mW

)

DSC scans at

1.5¬/20+ (K min¬1)

6¬/20+ (K min¬1)

10¬/20+ (K min¬1)

15¬/20+ (K min¬1)

20¬/20+ (K min¬1)

1.00 1.02 1.04 1.06 1.08

Y = 15.6659 ¬ 15.70492 X

Tfs/Tf

log(Q

/QS)

0

¬0.5

¬1.0

Figure 2 |DSC upscans at fixed 20Kmin−1 rates, following cooling atdifferent slower rates between 1.5 and 20Kmin−1. TheWang–Velikovmethod obtains the kinetics of the glass relaxation process by plotting thelog of the ratio (sample cooling rate/‘standard’ cooling rate (20Kmin−1))against the ratio of (standard fictive temperature (Tfs)/sample fictivetemperature), the latter being the value determined by the Fig. 1construction for the chosen cooling rate. Inset: Wang–Velikov Arrheniusplot24 in which both slope and intercept yield the ‘m fragility’ (the slope ofthe Arrhenius plot of the relaxation time versus Tg/T).

liquids, which is obviously associated with increasing relaxationtime, is also associated with a decreasing correlation length. Thereason for this expectation is obviously that lambda transitions,like other critical phenomena, have static correlation lengths thatare diverging at the critical point. It is particularly relevant thatthe relation between heat capacities across Tg and across a nearby(liquid–liquid) critical point has recently been established for amodel liquid system23 (see below).

Characterizing the glass transition in theCo50Fe50 systemThe technique used in our study is simple differential scanningcalorimetry (DSC), as described in the Methods section. We havestudied the relaxation kinetics in differentways, using scans throughTg in which the heating rates are the same as the original coolingrate, and both rates change from case to case (the originalMoynihanmethod), and have also applied the fictive temperature method ofref. 24, which uses a constant heating rate upscan after cooling atdifferent rates. The latter avoids any need for Tg determinationconstructions (maximum slope and so on) thatmight be susceptibleto instrument lag, and we have found it to be the most reliable(see Fig. 2 caption). The definition of the fictive temperature fromthe heating scan is shown for the lambda transition case, in Fig. 1,lower section. The ref. 24 method yields the fragility directly fromthe slope of the Arrhenius plot (Fig. 2, inset). This shows that,within experimental uncertainty, the ‘m fragility’ (or ‘steepnessindex’) is the ideal ‘strong’ liquid value of 16, correspondingto simple Arrhenius kinetics, notwithstanding the acceleratingconfigurational heat capacity seen in Fig. 1.

In a parallel study, we have defined a relaxation time fromthe start, and end, values of the glass transition, as described byBusch et al.

25,

τ =Tg(end)−Tg(start)/Q

where Q is the heating rate (in this method also the coolingrate) and found, again, simple Arrhenius behaviour, now with thepre-exponent 10−15 s. This is the ideally simple behaviour seenin the ‘strong’ limit of plastic crystals studied by Fujimori and

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ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS1823

Cp on a long timescale

Glycerol Hydrogen- bonded

Fragile

Strong

O-terphenyl

BeF2

SiO2

GeO2

1.0 1.2 1.4 1.6 1.8T/Tg

1.0

1.2

1.4

1.6

1.8

Cp

(liq

uid)

/ C

p (c

ryst

al)

Cp with rate 20 K min¬1

Cp with rate 1.5 K min¬1

Kirkwood approx.

Tg

400 600Temperature (K)

800 1,000

Fe50Co50

Bragg¬Williams theory

20

30

40

50

60

70

Cp

(J g

-ato

m¬1

K¬1

)

Figure 3 | Comparison of equilibrium heat capacities, derived from thescans of enthalpy recovery (shown in the Supplementary Information),with data obtained from fixed scan rate runs and also the theoreticalfunctions from the Bragg–Williams model and the Kirkwoodapproximation. Clearly if the energy barrier opposing the elementarylattice site exchange were smaller, the glass transition in the alloy wouldoccur at lower temperature and would quickly become difficult to detect, asin the case of most lambda transitions and also of dry vitreous silica, andvitreous water. The error bars reflect the distribution of multiple runs. Inset:Cp behaviour of some liquid-based glasses through Tg.

Oguni26—one of which (TlNO2) turns out to belong to the samelambda transition family as the present system (but one in whichthe ergodicity-breaking occurs only in the far tail of the transition,and is detectable only by precision adiabatic calorimetry).

To establish that it is indeed the lower part of the normal lambdatransition that is being chopped off by the glass transition of Fig. 1,we have carried out annealing processes at lower temperaturesfollowed by the enthalpy recovery scans27, which reveal the enthalpylost during the anneal (see Supplementary Information S1). Theattainment of equilibrium states was proved by demonstration ofannealing time independence. The heat capacity derived from thedifference between successive enthalpy recovery curve integrals isshown in Fig. 3. It is seen that (1) these form a natural continuationof the lambda form to lower temperatures, and (2) this form can bewell represented by the Kirkwood second-order approximation28.The Bragg–Williams approximation28 predicts a heat capacity peak,but quantitatively is quite inadequate.

Static correlation length considerationsNumerical simulations widely available for the two-dimensionalIsing model show that the correlation lengths for density andenthalpy fluctuations, which determine heat capacity, relaxationtimes and so on are all increasing as Tλ is approached bothfrom above and from below. The latter is to be emphasized: thecorrelation length increases as the temperature moves away fromthe ergodicity-breaking temperature,Tg. This is exactly the oppositetrend from that assigned to both static and dynamic correlationlengths of fragile glass formers11,13 as they approach their glasstransition temperatures from above.

Our aim, in this contribution, is to establish that this is thebehaviour to be expected from ‘strong’ as opposed to ‘fragile’liquids, and to show how this gives a new direction for thinkingabout the distinction between them. We do this in two steps usingmolecular dynamics modelling studies.

In the first step, we relate the lambda transition of Fig. 1 to thelambda transition in a simple liquid system that shows the samebehaviour as Fig. 1 at its liquid–liquid critical point. This is the

recently characterized ‘attractive Jagla model’ that has two distinctliquid phases, high density and low density, which become identicalat a liquid–liquid critical point, in analogy to the well-studiedcritical point for the two face-centred-cubic crystal phases of theelement cerium29. During cooling, the heat capacity of the single-phase liquid, along an isobar just above the critical pressure, showsa sharp critical-like peak, and then, like Fig. 1, passes through a glasstransition, trapping in the remaining disorder (see SupplementaryInformation S2 for a superposition). There can be little doubt that,as for Fe50Co50, the correlation length for enthalpy fluctuations inthe Jagla model is decreasing as T falls from the value at peakto the value at Tg. In ref. 23, this heat capacity peak is seen todecrease in height and spread out to high T , as the pressure movesincreasingly away from the critical point value (see SupplementaryInformation S2). The same occurs at the normal gas–liquid criticalpoint (see below). The line of peaks defines the ‘Widom line’30 as anextension of the coexistence line above Tc.

The change from fragile to strong liquid behaviour on crossingtheWidom line has been discussed for this case30, for the analogouscase of bulk water15,18,31 and in more detail for water in confinedgeometries32–34 (where crystallization does not occur, but wherewater–water interactions related to those in bulk evidently persist).The increasing static correlation length that accompanies thediverging heat capacity and compressibility during supercooling ofunconfined water—long a matter of controversy35,36—has recentlybeen confirmed by Nilsson and co-workers, using X-ray scatteringmethods37, now extended to −20 ◦C (Nilsson, A., presentation atISSP-11, Chiba, Japan, Oct 15, 2009). It has also been observed inthe fast-runningmWwatermodel ofMolinero andMoore38.

Connection to strong versus fragile liquid behaviourFor the second step extending this discussion to the classical strongliquids SiO2 and BeF2, we use ion dynamics studies16,17,39 andadditional experimental data40. We have already referred to thepeaks in heat capacity for BeF2 and SiO2 that are found whenhigh-T data from simulations are included, and now give moredetail. In particular, the heat capacity versus temperature calculatedat different fixed frequencies, in the silica study of Binder and co-workers16, shows an increasing ‘jump’ as the frequency is increased(and the temperature of the jump moves higher). This is similarto the behaviour observed in the present alloy system as the scanrate is increased. Furthermore, the temperature dependence of theenthalpy relaxation time, obtained from the temperature at whichthe imaginary part of the Cp function exhibited its peak value,reportedly follows an Arrhenius law with activation energy 5.6 eV(132 kcalmol−1; ref. 16) in remarkable accord with the activationenergy for laboratory viscosity (134 kcalmol−1; ref. 41).

Finally, in the simplest of the SiO2 models, molecular dynamicsstudies show39 that, in a family of P versus density isotherms,the low-temperature members are beginning to inflect, thatis, the behaviour is trending towards a liquid–liquid criticalpoint—as in the water and the more metal-like (more highlycoordinated23) Jagla models. Only inadequate computing timeprevented the observation of behaviour like that described abovefor the simpler (and fast-running) Jagla model. Certainly afragile-to-strong transition, consistent with an off-critical Widom-line crossing, has been identified in the kinetics of SiO2 inthe Beest–Kramer–van Santen model42 as well as in water15,18and confined water33,34. Furthermore, various metallic glassformers are now revealing fragile-to-strong transitions43,44 (seeSupplementary Information S3).

To provide quantitative diagrammatic support for this scenario,we present (in Fig. 4) experimental heat capacity data for thecase of BeF2 through its Tg and above its melting point to1,100 ◦C (ref. 45), together with molecular dynamics data athigher temperatures17, and compare it (and also SiO2 (ref. 16))

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NATURE PHYSICS DOI: 10.1038/NPHYS1823 ARTICLESH

eat c

apac

ity (

J g-a

tom

¬1 K

¬1)

T/Tg

Fe50Co50

Confined water SiO2 SiO2 BeF2 BeF2

ArgonPc = 4.86 MPaTc = 151 K

4.868 MPa

6.55 MPa

7.88 MPa9.45 MPa

11.82 MPa

Tc

168

336

Cp (

J mol

¬1 K

¬1)

116 144 172 200 228

Temperature (K)

25

50

75

100

125

0 1 2 3 4 5 6

Fe50Co50

Figure 4 |Heat capacities of BeF2 and SiO2 per g-atom through Tgcompared with those for Fe50Co50 and for confined water. Filled symbols:experiments; open symbols: simulations. The data sources are fullydocumented in Supplementary Information S4. Inset: The same smearingto high temperature is seen for the off-critical pressure behaviour oflaboratory argon near its gas–liquid critical point40 (see alsoSupplementary Information). Note that, in the laboratory, strong liquids arebeing observed only below the peak temperature, whereas fragile liquidsare observed only above it (water, the ‘Rosetta stone’ case, straddles thetwo domains when data above 0 ◦C are included).

with the data on the present system, and with data for confinedwater far below 0 ◦C (ref. 15)—and finally with data for theoff-critical heat capacity of an inert gas near its gas–liquid criticalpoint40. The similarity of the 11.82MPa argon data and that ofthe BeF2 and SiO2 high-temperature liquids is not easily ignored.The implication of this comparison is clearly that the behaviourof the classical inorganic network glasses is to be understoodin terms of off-critical (or ‘narrowly avoided critical’) pointphenomenology, lattice-gas models for the critical point havingmuch in common with models for lambda transitions in solids(see Supplementary Information S5). Furthermore, and of obvioustechnological significance, the static correlation lengths for density(refractive index) fluctuations in SiO2 glass must be a decreasingfunction of fictive temperature if we are correct.

The last point can be checked. Although the correlation lengthsare orders of magnitude smaller than the wavelength of laser light,the scattering of the laser light will be affected through the Fouriercomponents—and indeed, reduced light scattering in SiO2 coreglass fibres has been correlated with lower fictive temperatures46(see Supplementary Information S6). It is likewise observed that,for confined water, the dynamic susceptibility χT(Q,t ), determinedby neutron scattering34 and linked to the correlation length fordynamic heterogeneity11,34, decreases for temperatures below theheat capacity peak (Supplementary Information S7)—although thatfor the corresponding four-point correlator does not. The latter isevidently the case for SiO2 also47.

Relation of static correlation lengths to relaxationThere is a clear implication in our discussion that the fluctuationsthat peak in correlation length at the critical point, or at least at theWidom line, are those that are influencing the structural relaxationtime and hence are somehow involved in the glass transition, butcan this be justified? It is difficult to imagine otherwise in the caseof Fe50Co50 where the site exchange ordering process is so clear,although the ergodicity breaking is occurring in spite of, ratherthan because of, the decreasing correlation length. For liquids itis not so obvious. There are many different fluctuations and at

least those for enthalpy and density are statistically independent.Indeed, for fragile liquids, the excess heat capacity and the excesscompressibility behave very differently as T approaches Tg (seeSupplementary Information S8). Our attention has been on Cp,hence on the enthalpy fluctuations. These are the ones implied bythe success of the Adam–Gibbs entropy equation, which (unlikethe free volume equation) has been validated by so many liquidsimulations as well as experimental studies. They are also theones that Qiu et al.

8 singled out in explanation of their dynamiccorrelation length observations.

To summarize, the study of the glass-like transition in theCo50Fe50 superlattice lambda transition provides an experimentalparallel to the recent reports of glass transitions on the low-temperature flank of the supercritical heat capacity spike in amodelliquid system (Jagla model) that possesses a liquid–liquid criticalpoint. Both provide examples of glass transitions with large heatcapacity signatures, accompanied by correlation length decreases asTg is approached from above. There is a strong suggestion that thisis related to ‘strong’ liquid behaviour in the classical network glass-former systems, which then implies that strong and fragile liquidsexist on opposite flanks of an underlying order–disorder transition(the critical pressure for which may, however, lie far from theexperimental isobar, and may be unobservable, for example, in thetension domain). In the very fragile liquid cases, according to theo-retical fittings of excess Cp and entropy data48, this continuous pro-cess is interrupted by a first-order transition to the low-entropy statethat occurs a little below Tg (that is, on long observation times)20,48and may be related to the ‘Ediger phases’ now being observed invapour deposition studies49,50 (see Supplementary Information S9).

MethodsThe Fe50Co50 alloy was prepared by arc melting ultrasonically cleansed Fe andCo pieces, of purity of 99.97% and 99.95%, respectively, in a high-purity argonatmosphere. After remelting under argon and casting into water-chilled coppermoulds (5mmbore), the as-cast alloy rod was cut into 1mmdiscs, using a diamondsaw, and sealed into high-purity gold DSC pans. Calorimetry was carried out usinga Perkin-Elmer diamond differential scanning calorimeter under a constant flow(20mlmin−1) of high-purity argon. For the fictive temperature determinations,cooling rates were chosen not to exceed the fixed 20Kmin−1 heating rate. Datapoints obtained at cooling rates greater than 20Kmin−1 in the fictive temperaturemeasurements (and at scan rates greater than 20Kmin−1 in the relaxation timemeasurements) were considered unreliable, owing to insufficient temperatureequilibration, and have not been included in the assessment of the kinetics.

Received 30 April 2010; accepted 24 September 2010;published online 28 November 2010

References1. Angell, C. A. Formation of glasses from liquids and biopolymers. Science 267,

1924–1935 (1995).2. Busch, R, Schroers, J & Wang, W. H. Thermodynamics and kinetics of bulk

metallic glass.MRS Bull. 32, 620–623 (2007).3. Martinez, L. M. & Angell, C. A. A thermodynamic connection to the fragility

of glass-forming liquids. Nature 410, 663–667 (2001).4. Wang, L-M., Richert, R. & Angell, C. A. Fragility and thermodynamics in

non-polymeric glassformers. J. Chem. Phys. 125, 074506 (2006).5. Richert, R. Heterogeneous dynamics in liquids: Fluctuations in space and time.

J. Phys. Condens. Matter 14, R703–R738 (2002).6. Ediger, M. D. Spatially heterogeneous dynamics in supercooled liquids.

Ann. Rev. Phys. Chem. 51, 99–128 (2000).7. Donati, C., Glotzer, S. C. & Poole, P. H. Growing spatial correlations of particle

displacements in a simulated liquid on cooling toward the glass transition.Phys. Rev. Lett. 82, 5064–5067 (1999).

8. Qiu, X. H. & Ediger, M. D. Lengthscale of dynamic heterogeneity insupercooled d-sorbitol: Comparison to model predictions. J. Phys. Chem. 107,459–464 (2003).

9. Donati, C. et al. Growing spatial correlations of particle displacements in asimulated liquid on cooling toward the glass transition. Phys. Rev. Lett. 82,5064–5067 (1999).

10. Reinsberg, S. A., Qui, X. H., Wilhelm, M., Spiess, H. W. & Ediger, M. D.Length scale of dynamic heterogeneity in supercooled glycerol near Tg.J. Chem. Phys. 114, 7299–7302 (2001).

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© 2011 Macmillan Publishers Limited. All rights reserved.

ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS1823

11. Berthier, L. et al. Direct experimental evidence of a growing length scaleaccompanying the glass transition. Science 310, 1797–2000 (2005).

12. Moynihan, C. T. & Schroeder, J. Non-exponential structural relaxation,anomalous light scattering and nanoscale inhomogeneities in glass formingliquids. J. Non-Cryst. Solids 160, 52–59 (1993).

13. Tanaka, H., Kawasaki, T., Shintani, H. & Watanabe, K. Critical-like behaviorof glass-forming liquids. Nature Mater. 9, 324–331 (2010).

14. Angell, C. A. & Ueno, K. Soft is strong. Nature 462, 45–46 (2009).15. Angell, C. A. Insights into phases of liquid water from study of its unusual

glass-forming properties. Science 319, 582–587 (2008).16. Scheidler, P., Kob, W., Latz, A., Horbach, J. & Binder, K. Frequency-dependent

specific heat of viscous silica. Phys. Rev. B 63, 104204 (2005).17. Hemmati, M., Moynihan, C. T. & Angell, C. A. Interpretation of the molten

BeF2 viscosity anomaly in terms of a high temperature density maximum, andother waterlike features. J. Chem. Phys. 115, 6663–6671 (2001).

18. Ito, K., Moynihan, C. T. & Angell, C. A. Thermodynamic determination offragility in liquids and a fragile-to-strong liquid transition in water. Nature398, 492–495 (1999).

19. Kaya, S. & Sato, H. Superstructuring in the iron–cobalt system and theirmagnetic properties. Proc. PhysicoMath. Soc. Jpn 25, 261–273 (1943).

20. Angell, C. A. Glass formation and glass transition in supercooled liquids, withinsights from study of related phenomena in crystals. J. Non-Cryst. Solids 354,4703–4712 (2008).

21. Moynihan, C. T., Easteal, A. J., Debolt, M. A. & Tucker, J. Dependenceof fictive temperature of glass on cooling rate. J. Amer. Ceram. Soc. 59,12–16 (1976).

22. Yue, Y. Z., von der Ohe, R. & Jensen, S. L. Fictive temperature, cooling rate,and viscosity of glasses. J. Chem. Phys. 120, 8053–8059 (2000).

23. Xu, L-M., Buldyrev, S. V., Giovambattista, N., Angell, C. A. & Stanley, H. E.A monatomic system with a liquid–liquid critical point and two glassy states.J. Chem. Phys. 130, 054505 (2009).

24. Wang, L. M., Velikov, V. &Angell, C. A.Direct determination of kinetic fragilityindices of glassforming liquids by differential scanning calorimetry: Kineticversus thermodynamic fragilities. J. Chem. Phys. 117, 10184–10192 (2002).

25. Busch, R., Bakke, E. & Johnson, W. L. Viscosity of the supercooled liquid andrelaxation at the glass transition of the Zr46.75Ti8.25Cu7.5Ni10Be27.5 bulk metallicglass forming alloy. Acta Mater. 46, 4725–4732 (1998).

26. Fujimori, H. & Oguni, M. Correlation index (Tga −Tgb)/Tg and activationenergy ratio as parameters characterising the structure of liquid and glass.Solid State Commun. 94 (1995).

27. Busch, R. & Johnson, W. L. The kinetic glass transition of theZr46.75Ti8.25Cu7.5Ni10Be27.5 bulk metallic glass former-supercooled liquids on along timescale. Appl. Phys. Lett. 72, 2695–2697 (1998).

28. Girifalco, L. A. Statistical Mechanics of Solids (Oxford Univ. Press, 2000).29. Lipp, M. J. et al. Thermal signatures of the Kondo volume collapse in cerium.

Phys. Rev. Lett 101, 165703 (2008).30. Xu, L.-M. et al. Relation between the Widom line and the dynamic crossover

in systems with a liquid–liquid phase transition. Proc. Natl Acad. Sci. USA 102,16558–16562 (2005).

31. Angell, C. A. Water II is a strong liquid. J. Phys. Chem. 97, 6339–6341 (1993).32. Mallamace, F. et al. The fragile-to-strong dynamic crossover transition in

confined water: Nuclear magnetic resonance results. J. Chem. Phys. 124,161102 (2006).

33. Liu, L. et al. Pressure dependence of fragile-to-strong transition and a possiblesecond critical point in supercooled confined water. J. Chem. Phys. 95,117802 (2005).

34. Zhang, Y. et al. Dynamic susceptibility of supercooled water and its relation tothe dynamic crossover phenomenon. Phys. Rev. E 79, 040201 (2009).

35. Bosio, L., Teixeira, J. & Stanley, H. E. Enhanced density fluctuations in wateranalysed by neutron scattering. Phys. Rev. Lett. 46, 597–600 (1981).

36. Xie, Y. et al. Noncritical behaviour of density fluctuations in supercooled water.Phys. Rev. Lett. 71, 2050–2053 (1993).

37. Huang, C. et al. The inhomogeneous structure of water at ambient conditions.Proc. Natl Acad. Sci. USA 106, 15214–15218 (2009).

38. Moore, E. B. & Molinero, V. Growing correlation length in supercooled water.J. Chem. Phys. 130, 244505 (2009).

39. Poole, P. H., Hemmati, M. & Angell, C. A. Comparison of thermodynamicproperties of simulated liquid silica and water. Phys. Rev. Lett. 79,2281–2284 (1997).

40. Kim, K. Y. Calorimetric Studies on Argon and Hexafluoro Ethane and aGeneralized Correlation of Maxima in Isobaric Heat Capacity 20. (1974),(Technical report, Department of Chemical Engineering, Michigan University)http://deepblue.lib.umich.edu/handle/2027.42/6003.

41. Bockris, J. O., McKenzie, J. D. & Kitchener, J. A. Viscous flow in silica andbinary liquid silicates. Trans. Faraday Soc. 51, 1734–1748 (1955).

42. Saika-Voivod, I., Poole, P. H. & Sciortino, F. Fragile-to-strong transitionand polyamorphism in the energy landscape of liquid silica. Nature 412,514–517 (2001).

43. Way, C., Wadhwa, P. & Busch, R. Influence of shear rate and temperatureon the viscosity and fragility of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 metallicglass-forming liquid. Acta Mater. 55, 2977–2983 (2007).

44. Zhang, C., Hu, L., Yue, Y-Z. & Mauro, J. C. Fragile-to-strong transition inmetallic glass-forming liquids. J. Chem. Phys. 133, AN014508 (2010).

45. Tamura, S., Yokokawa, T. &Niwa, K. J. Enthalpy of beryllium fluoride from 456to 1,083 K by transposed temperature drop calorimetry. J. Chem. Thermodyn.

7, 633–643 (1975).46. Sakaguchi, S. & Todoroki, S-I. Raleigh scattering of silica core optical fiber after

heat treatment. Appl. Opt. 37, 7708–7711 (1998).47. Berthier, L. Revisiting the slow dynamics of a silica melt using Monte Carlo

simulations. Phys. Rev. E 76, 011507 (2007).48. Matyushov, D. & Angell, C. A. Gaussian excitations model for glassformer

thermodynamics and dynamics. J. Chem. Phys. 126, AN094501 (2007).49. Dawson, K. J., Kearns, K. L., Yu, L. & Ediger, M. D. Physical vapor deposition

as a route to hidden amorphous states. Proc. Natl Acad. Sci. USA 106,15165–15170 (2009).

50. Ishii, K., Nakayama, H., Hirabayashi, S. & Moriyama, R. Anomalouslyhigh-density glass of ethylbenzene prepared by vapor deposition attemperatures close to the glass-transition temperature. Chem. Phys. Lett. 459,109–112 (2008).

AcknowledgementsWe appreciate support received from the Deutsche Forschungsgemeinschaft (DFG).C.A.A. acknowledges helpful discussions withM.D. Ediger and JY-Z. Yue.

Author contributionsC.A.A. and R.B. conceived the project, I.G. and S.W. planned and carried out theexperimental work, S.W. and I.G. analyzed the data, and C.A.A. wrote the paper withimportant literature and diagrammatic input fromS.W. and advice from I.G. andR.B.

Additional informationThe authors declare no competing financial interests. Supplementary informationaccompanies this paper on www.nature.com/naturephysics. Reprints and permissionsinformation is available online at http://npg.nature.com/reprintsandpermissions.Correspondence and requests formaterials should be addressed to C.A.A.

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